1. Field of the Invention
The present invention relates to a feedback control for scanning tunneling microscopes or the like. Specifically, the feedback control of the present invention uses stored topographical information to increase the response of the feedback loop.
2. Description of the Prior Art
In a typical scanning tunneling microscope, a conducting tip is positioned an atomic distance such as 2 to 3 atoms above the surface of a sample. The sample is typically a conductor or a semiconductor. This distance of 2 to 3 atoms is approximately ten angstroms (10 .ANG.). A current which is referred to as the tunneling current may then be made to flow between the sample and the tip. This tunneling current is due to a bias voltage applied between the sample and the tip.
The tip is typically scanned over the surface of the sample using a raster scan formed by a plurality of adjacent horizontal scan lines and with a feedback loop positioning the vertical position of the tip. Specifically, the vertical position of the tip is controlled so that the tunneling current is held to a constant value. The vertical position of the tip is normally controlled by a piezoelectric element. In particular, the tip is mounted on the piezoelectric element and by applying positive and negative voltages to the piezoelectric element, the element expands or contracts to thereby lower or raise the tip relative to the sample. The maintaining of a constant tunneling current through the use of the feedback loop thereby gives a constant height of the tip above the surface.
The maintaining of the constant tunneling current is accomplished through the positive or negative voltage applied to the piezo element which voltage may be referred to as a positioning voltage. Therefore, by monitoring the positioning voltage which is applied to the vertical positioning piezo element, the vertical position of the tip can be recorded since it is related to the positioning voltage. In this way, the vertical position of the tip is recorded as the tip is scanned along the surface to provide a record of the vertical position of the sample surface as a function of the horizontal position of the tip relative to the sample. The horizontal coordinates of the tip are normally referred to as X and Y, and the vertical position is referred to as Z. It is, therefore, possible to get a record of the topography of the surface by monitoring the X and Y position of the scanning of the tip and at the same time monitoring the Z position of the height of the tip.
It is very important for all scanning tunneling microscopes that the feedback loop controlling the Z position of the tip relative to the sample be very precise. This is because the current that flows between the sample and the tip occurs only when the tip is about ten angstroms (10 .ANG.) from the surface. As the tip is moved away from the surface, the tunneling current falls off exponentially and can drop by a factor such as five (5) as the tip is moved a very short distance such as five or more angstroms (5 .ANG.) from the surface. Normally, a scanning tunneling microscope cannot be operated with the tip much further away from the surface than twenty angstroms (20 .ANG.) because at that time, the tunneling current becomes too small to measure.
It can be seen, therefore, that the vertical position of the tip must be precisely controlled with the tip very close to the surface. In one direction, the control must be very close, but without hitting the tip on the surface, or as indicated above, without the tip getting so far from the surface that the tunneling current drops to an immeasurable level. In order to accomplish this and thereby map the topography of a sample with the scanning tunneling microscope, the feedback loop controlling the vertical position of the tip must be both precise and fast, but without causing oscillation. It is also desirable that the scanning of the samples be with scans of relatively large dimensions. If these larger scans are to be performed in the same time period, then the feedback loop must be faster in order to follow the topography. If this cannot be accomplished, then the scan rate must be slowed down in order to provide for the larger scans, but this is undesirable since the scan would, therefore, take considerably greater periods of time. In general, the faster the scan rate, the better.
The newer scanning tunneling microscopes allow for relatively large scans such as nine microns by nine microns. It is desirable to provide for such large scans within reasonably short periods of time such as under one minute. In order to accomplish this, the required scan rate would be very difficult to achieve and still have the tip follow the surface with the required accuracy.
In general, most scanning tunneling microscopes that are in the prior art use an analog feedback loop for the loop controlling the vertical position of tip. In such an analog signal, an error signal is produced which is the difference between a set point current and the actual tunneling current flowing between the sample and the tip. This error signal is used in the feedback loop to change the position of the tip to correct the value of the tunneling current back to the set point value as the tip is scanned across the surface. As an example, if the tip moves too close to the surface, the tunneling current will have a value above the set point value and the feedback loop will receive an error signal reflective of the difference, amplify the error signal and apply it to the vertical drive element with the proper polarity to raise the tip from the surface. When the tip is raised from the surface, this in turn lowers the value of the tunneling current back to the set point value.
The type of feedback generally used in prior art scanning tunneling microscopes is both integral and proportional. The integral portion of the feedback keeps the average error always zero, but tends to slow down the response of the feedback loop since integrators smooth out rapid variations in the error signal. Additionally, the use of an integrator produces a phase shift of 90.degree. which is somewhat detrimental in the feedback loop. For example, it can be seen that if the phase shift where 180.degree., the tip would be completely out of phase with the tunneling current and the feedback would drive the tip in the direction opposite to that required to correct the error and the loop would oscillate.
Although a 90.degree. phase shift is not that extreme, it does produce a detriment in the feedback loop. In addition, if there if is a sinusoidal variation in the error signal due to a sinusoidal surface for the sample, then it is necessary to provide a sinusoidal variation of the vertical tip position to correct the error signal. Phase shifts in the feedback loop and in particular 180.degree. phase shifts can have the tip driven in the wrong direction and with the whole feedback oscillating. As a further requirement for stable operation of the feedback loop, the gain of the feedback loop must be kept down to a reasonable level.
In order to mitigate the above described problems in prior art feedback loops, these prior art feedback loops include proportional feedback in which the error signal itself is used in addition to the integrated error in the feedback loop. For example, if there is an error in the tunneling current, this error is amplified and also applied to the positioning of the tip. This proportional feedback has the advantage that there is no inherent phase shift associated with it and, therefore, the feedback loop is less sensitive t the accumulation of phase shifts from other parts of the feedback loop such as the filters, amplifiers and tip drive elements. The use of proportional feedback also gives a higher frequency response than the integral feedback.
The different forms of feedback described above are used in prior art scanning tunneling microscopes to form a local error signal in the feedback loop. Specifically, the error signal measured at the present horizontal position of the tip is used to control the vertical position of the tip at essentially that same horizontal position so as to maintain the constant tunneling current. If the topography of the sample is very steep, then the local error signal becomes large and unless the gain of the feedback loop is very high, the vertical position of the tip may not be corrected fast enough and the tip would thereby run into the surface. This condition obviously must be avoided. If the tip runs into the surface of the sample, this will completely upset the feedback loop and result in an improper image.
So far an analog feedback loop has been described, but it is to be appreciated that the feedback loop may also be formed as a digital feedback loop. In such a digital feedback loop, the tunneling current between the sample and the tip is digitized and entered into a computer where the digital value of the tunneling current is compared with a preset value to calculate what the vertical position of the tip should be in order make the error signal become zero. One advantage of the use of a digital feedback is that digital processing may now be available. With such digital processing, any function of the error signal can be applied within the feedback loop. For example, it is possible with a digital feedback loop to use, in addition to the integral and proportional feedback, other forms of feedback such as differential feedback. In general, however, the use of a digital feedback loop has accomplished the same general results as the prior art analog feedback loops, except that the integrators and amplifiers that are found in analog feedback loops are replaced by numerical calculations in the computer.
Basically, both analog and digital feedback loops for scanning tunneling microscopes both have the common problem of requiring the feedback loop to have a high frequency response in order to provide for accurate tracking of the sample surface. In addition, any phase delays may lead to instabilities in the feedback response especially at high frequencies and when the gain is high. All of these problems have limited the use of scanning tunneling microscopes and specifically, have required relatively slow scan rates in order to provide for image enhancement. In particular this is true when the size of the scans are made larger and where it is desired to accomplish these larger scans in a reasonable period of time. It is, therefore, desirable to provide for improvements in the feedback control for scanning tunneling microscopes to overcome a number of the problems described above in the prior art devices.